(Difficult)
In 16.2.3 the author discusses how we can take a plaintext (single numerical value) and represent such a message in an elliptic curve. I see how the example worked, but I had a few questions about details on finding the elliptic curve representation:
1.) If we are not guaranteed that the message will work on the elliptic curve, wouldn't that limit the use of elliptic curves for cryptographic purposes?
2.) When looking at elliptic curves we are dealing with square roots, so is there a standard by which we decide which square root to pick?
(Reflective)
In 16.2.2 we look at the example of a "discrete log" on elliptic curves. The author discusses briefly the difficulties of attacking a discrete log problem on elliptic curves, but nothing is mentioned as to the use of discrete logs on elliptic curves for cryptography. The lecture leads us to believe it would provide us with a fairly secure method of encryption, but does not give us details on how it would work. Is our main focus on elliptic curves used for a factorization method, or will we be using elliptic curves as a method of encryption as well?
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